Non-Empirical Interactions for the Nuclear Shell Model: An Update (1902.06154v3)

Abstract: The nuclear shell model has been perhaps the most important conceptual and computational paradigm for the understanding of the structure of atomic nuclei. While the shell model has been predominantly used in a phenomenological context, there have been efforts stretching back over a half century to derive shell model parameters based on a realistic interaction between nucleons. More recently, several ab initio many-body methods---in particular many-body perturbation theory, the no-core shell model, the in-medium similarity renormalization group, and coupled cluster theory---have developed the capability to provide effective shell model Hamiltonians. We provide an update on the status of these methods and investigate the connections between them and potential strengths and weaknesses, with a particular focus on the in-medium similarity renormalization group approach. Three-body forces are demonstrated to be an important ingredient in understanding the modifications needed in phenomenological treatments. We then review some applications of these methods to comparisons with recent experimental measurements, and conclude with some remaining challenges in ab initio shell model theory.

Overview of Non-Empirical Interactions for the Nuclear Shell Model

The nuclear shell model has played a pivotal role in elucidating the structure of atomic nuclei, serving as a primary framework for analyzing nuclear interactions. This paper by Stroberg et al. provides an update on the theoretical developments concerning non-empirical interactions within the shell model. It explores several ab initio many-body methods, emphasizing the significance of the in-medium similarity renormalization group (IMSRG) approach in advancing our understanding and modeling of nuclear forces.

Many-Body Methods

Recent progress in computational nuclear physics has facilitated the derivation of shell model parameters from realistic nucleon interactions, employing advanced ab initio methods. These methods include many-body perturbation theory, no-core shell model (NCSM), coupled cluster theory, and the IMSRG. Each method provides distinctive capabilities for forming effective shell model Hamiltonians, demonstrating varying strengths in capturing the complex interplay of nuclear forces.

The paper highlights the particular focus on IMSRG, detailing its application to derive shell model interactions without resorting to phenomenological adjustments. IMSRG operates by transforming the microscopic interaction through similarity transformations, effectively decoupling high and low-energy degrees of freedom. This transformation allows for the retention of crucial many-body correlations, such as three-body forces, thus providing a more comprehensive view of nuclear interactions.

Role of Three-Body Forces

Three-body forces emerge as a significant component in refining shell model interactions. They are particularly important in addressing deficiencies in phenomenological treatments by offering explanations for otherwise disparate empirical adjustments. The paper emphasizes the necessity of incorporating these forces through techniques like ensemble normal ordering to achieve accuracy aligned with experimental observations.

Applications and Challenges

The paper provides insights into various applications across different regions of the nuclear chart, showcasing the advances made possible by these methods. For example, the location of the neutron drip line in oxygen isotopes—a phenomenon long challenging accurate modeling—can now be explained by three-body forces utilizing the IMSRG approach.

However, challenges remain, notably in accurately modeling electromagnetic transitions and addressing the intruder-state problem. Electromagnetic transitions pose difficulties due to the sensitivity of collective modes, which are not adequately captured under current model truncations. The intruder-state problem, seen in regions such as the "islands of inversion," suggests that single major shell models may not be sufficient for accurately representing ground states, necessitating further theoretical advancements.

Implications for Nuclear Physics

The implications of these developments extend both practically and theoretically in nuclear science. From a practical standpoint, the refined conceptual understanding of three-body forces and their integration into computational models enhances predictive capability, which is vital for future experimental alignment. Theoretically, the advancement of these methodologies reinforces the foundation of nuclear physics rooted in quantum chromodynamics, aiding in the pursuit of a universal nuclear Hamiltonian.

Looking forward, the exploration of theoretical frameworks such as effective field theory (EFT) for the shell model might provide new avenues for systematic improvements. Furthermore, uncertainty quantification remains an open area requiring rigorous attention to integrate predictive assurance into theoretical calculations.

In conclusion, while foundational strides have been made toward non-empirical interactions in the nuclear shell model, ongoing challenges motivate further exploration and refinement, holding the promise of significantly enhancing our understanding of nuclear structure and interactions.